In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, Honeyside is the house you’ll be able to purchase in Riften once you gain enough favor with the Jarl there, and costs 8,000 gold.
To buy Honeyside, you do an assortment of quests in the city of Riften. There are quite a few, so talk to everyone and do every quest in Riften you can find (minus the Thieves Guild quests, they aren’t required). Once you think you’ve done all of them, look for Wujeeta at the docks outside of Riften. She’ll give you a quest, which will open up quests for the Jarl about stopping the Skooma trade. Once you complete those, you’ll become a Thane, and you’ll be able to purchase Honeyside from the Jarl’s adviser Anuriel for 8,000 gold.
Anuriel is also the one you’ll be dealing with to upgrade your home as well.